Test Index

WAEC Further Mathematics 2023 Paper

Question : 16

Total: 40

The table shows the mark obtained by students in a test.

Solution:

Concept:

The arithmetic mean is the total of all values divided by the total frequency, using the formula

\bar{x} = \frac{\sum fx}{\sum f}

Explanation:

Let the unknown frequency for mark

2

k

The mean is given as

3

, so

\frac{\sum fx}{\sum f} = 3

Now compute

\sum fx

(1 \times 2) + (2 \times k) + (3 \times 1) + (4 \times 1) + (5 \times 2)

= 2 + 2k + 3 + 4 + 10 = 19 + 2k

Compute

\sum f

2 + k + 1 + 1 + 2 = 6 + k

Substitute into the mean formula:

\frac{19 + 2k}{6 + k} = 3

Multiply both sides by

6 + k

19 + 2k = 3(6 + k)

Expand:

19 + 2k = 18 + 3k

Rearrange:

2k - 3k = 18 - 19

, so

-k = -1

Hence,

k = 1

Answer:

k = 1

, which corresponds to Option B.

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